On tensor product L-functions and langlands functoriality

In the spirit of the Langlands proposal on Beyond Endoscopy, we discuss the explicit relation between the Langlands functorial transfers and automorphic L-functions. It is well-known that the poles of the L-functions have deep impact to the Langlands functoriality. Our discussion also includes the meaning of the central value of the tensor product L-functions in terms of the Langlands functoriality. This leads to the theory of the twisted automorphic descents for cuspidal automorphic representations of general classical groups.